Sentiment towards perceived riskier currencies was muted after European ministers made little progress overnight towards using the bloc's rescue funds to combat soaring Spanish and Italian borrowing costs.
The euro fell 0.1 percent against the pound to 79.22 pence, near a low of 79.06 hit on Monday, its weakest level since November 2008.
Against the safe-haven dollar, sterling dipped 0.1 percent to $1.5505, holding steady despite retail sales and house price data released earlier on Tuesday that reflected a weakening British economy.
"The numbers were pretty poor, spelling the story of a slowing economy, but they've not had a massive impact on sterling," said Simon Derrick, head of currency research at Bank of New York Mellon.
British retail sales rose 1.4 percent in June, the British Retail Consortium said, far below the 2 percent estimated by analysts, while UK house prices fell more than expected.
The UK economy was poised for more bad news with British industrial output data for May, to be released at 0830 GMT, expected to show a 0.2 percent month-on-month decline, according to a Reuters poll.
But Derrick said more bearish data had largely been priced into the market, and an output fall closer to 1 percent would be required to prompt a significant move in sterling.
The market will also scrutinise minutes from last month's meeting of the US Federal Reserve, to be published on Wednesday. Any indication the Fed may opt for another round of asset buying before the end of the year is likely to weigh on the dollar versus sterling.